Question

A polygon has (n) sides and three of its exterior angles are 85, 76 and 46 the remaining (n-3) exterior angles are Each of 17, calculate the value of n.
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It is related to ANGLE PROPERTIES OF POLYGONS.

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Answer 1

Answer:

Polygon has  11  sides

Step-by-step explanation:

Sum of the exterior angles of any polygon is always 360 ∘

As three angles are  70 ∘ ,80 ∘ and 90 ∘ and remaining  n − 3 angles are  15 ∘ and their sum is  360 ∘ ,we have

70+ 80 + 90 + 15 ( n − 3)= 360

or  15( n − 3 ) = 360 − 70 − 80 − 90 = 120

and  n − 3 = 120 ÷15 = 8

i.e.  

n = 11

Hence, polygon has  

11  sides